Consistent quadrangulation for shape collections via feature line co-extraction

This paper presents a method that takes a collection of 3D surface shapes, and produces a consistent and individually feature preserving quadrangulation of each shape. By exploring the correspondence among shapes within a collection, we coherently extract a set of representative feature lines as the key characteristics for the given shapes. Then we compute a smooth cross-field interpolating sparsely distributed directional constraints induced from the feature lines and apply the mixed-integer quadrangulation to generate the quad meshes. We develop a greedy algorithm to extract aligned cut graphs across the shape collection so that the meshes can be aligned in a common parametric domain. Computational results demonstrate that our approach not only produces consistent quad meshes across the entire collection with significant geometry variation but also achieves a trade-off between global structural simplicity for the collection and local geometry fidelity for each shape.